Argyros, Ioannis K and Geroge, Santhosh and Erappa, Shobha M (2018) Extending the Applicability of Newton’s and Secant Methods Under Regular Smoothness. Boletim da Sociedade Paranaense de Matematica, 3 (5). pp. 1-16. ISSN 0037-8712

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Abstract

The concept of regular smoothness has been shown to be an appropriate and powerfull tool for the convergence of iterative procedures converging to a locally unique solution of an operator equation in a Banach space setting. Motivated by earlier works, and optimization considerations, we present a tighter semi-local convergence analysis using our new idea of restricted convergence domains. Numerical examples complete this study.

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